[issue44344] Documentation for pow() should include the possibility of complex numbers as a return type

[Mark Dickinson]

Mark Dickinson <dickinsm at gmail.com> added the comment:

[Dennis]

> I think the relevant property is that the exponent is not an integer

Yep: the delegation to complex pow kicks in after handling infinities and nans, and only for strictly negative base (-0.0 doesn't count as negative for this purpose) and non-integral exponent.

Here's the relevant code: https://github.com/python/cpython/blob/257e400a19b34c7da6e2aa500d80b54e4c4dbf6f/Objects/floatobject.c#L773-L782

To avoid confusion, we should probably not mention fractions like `1/3` and `4/3` as example exponents in the documentation, since those hit the What-You-See-Is-Not-What-You-Get nature of binary floating-point. Mathematically, `z^(1/3)` is a very different thing from `z^(6004799503160661/18014398509481984)` for a negative real number `z`, and the latter is what's _actually_ being computed with `z**(1/3)`. The advantage of the principal branch approach is that it's continuous in the exponent, so that `z^(1/3)` and `z^(6004799503160661/18014398509481984)` only differ by a tiny amount.

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nosy: +mark.dickinson

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<https://bugs.python.org/issue44344>
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